Ms. Juan / 8th period / Team #2

Linear Equations

100

Aaron is 5 years younger than Ron. Four years later, Ron will be twice as old as Aaron. Find their present ages

 x + 4 = 2(x - 5 + 4)

⇒ x + 4 = 2(x - 1)

⇒ x + 4 = 2x - 2

⇒ x + 4 = 2x - 2

⇒ x - 2x = -2 - 4

⇒ -x = -6

⇒ x = 6

Therefore, Aaron’s present age = x - 5 = 6 - 5 = 1

200

The length of a rectangle is twice its breadth. If the perimeter is 72 meter, find the length and breadth of the rectangle.

2(x + 2x) = 72

⇒ 2 × 3x = 72

⇒ 6x = 72

⇒ x = 72/6

⇒ x = 12

We know, length of the rectangle = 2x

                      = 2 × 12 = 24

300

The difference between the two numbers is 48. The ratio of the two numbers is 7:3. What are the two numbers?

7x - 3x = 48

⇒ 4x = 48

⇒ x = 48/4

⇒ x = 12

Therefore, 7x = 7 × 12 = 84

          3x = 3 × 12 = 36

400

The freshmen plans to sell sweatshirts and t-shirts with the school mascot printed on the front. The function y= -1.5+22.5 indicates the possible numbers if sweatshirts?

a. 22; the greatest number of t-shirts the class can buy 

b. -1.5; the coefficient number of x in the function 

c. 15; the greatest number of sweatshirt

          0=1.5x+22.5

 0+1.5x=-1.5x+1.5x+22.5

      1.5x=22.5

       1.5x  22.5

=15    answer is C.       

500

Verify algebraically that -1 is the zero of f(x)=3x+3?

f(x)= 3x+3

f(x)=3(1)+3

f(x)=-3+3

f(x)=0

System of equations

100

What is the solution to the equation

y=-3x+10

y=x-2

(3,1)

200

What is the solution to the equation

2x-y=-1

4x-2y=6

no solution. The system is inconsistent

300

What is the solution to the equation

y+4x=8

5x+2y=13

(x,y)=(-2,5)

400

What is the solution to the equation

2x+2y=6

12=2y-x

(x,y)=(-2,5)

500

What is the solution to the equation

4y+2x=5

x=8-2y

no solution

exponential functions

100

solve 10^1-x=10⁴

x=-3

200

solve 3^x=9

x=2

300

solve 5^x=5³

x=3

400

solve 2^x=-4

no solution

500

solve 3^2x-1=27

x=2